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I am solving general black-box optimization problems like: x*: f(x) -> min, where x are permutations of length N (N = 50 for example, so brute force search is not possible). … But, most of these methods use always some kind of local search, which require suitable distance metric at search space (space of permutations x in my case). …

I have restriction (0,1) matrix to restrict which item (column index) can be on current position (row index) at permutations. … For example: 4x4 case (4 position permutations) 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 So, on position 4 (4th row at restriction matrix) is not allowed items …

So far I am using Hungarian's assignment algorithm to produce random permutations consistent with restriction matrix $R$, but these permutations are significantly non-uniformly sampled. … If $R$ contains only ones, $\Pi_R$ is the set of all permutations. …

Some comments here states that interpretation of matrix $P$ and permutations probability $p(\pi)$ are not clear enough to define unique permutations distribution. … The problem how to effectively generate (0,1) restricted permutations (permutations with restricted positions) is different problem. …

I have the following problem: I need to generate $\ell$ random permutations each of length $n$ from a list of $m$ elements ($m \ge n$) by a predefined probability matrix $P$ of size $n$ x $m$. … Permutations are parametrized via probability matrix P. The probability matrix P is generated by black-box objective function responses. …